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Консультация № 192149
Обсуждение
18.12.2017, 15:06
общий
это ответ
Здравствуйте, CTEKLO!
Вот таким образом можно решить
Вот таким образом можно решить
Прикрепленные файлы:
5
18.12.2017, 16:22
общий
это ответ
Здравствуйте, CTEKLO!
Обозначим [$8730$](x + 5) = y. Эта переменная удовлетворяет уравнению y2 - 5 = x и должна быть неотрицательной.
Система уравнений
y = x2 - 5, x = y2 - 5
эквивалентна исходному уравнению при условии y >= 0.
Вычитая из первого уравнения второе, получим
y - x = (x-y)(x+y), т.е,, должно быть либо y = x, либо y = -x - 1.
В первом случае имеем квадратное уравнение x2 - x - 5 = 0,
у которого отрицательный корень нужно отбросить, т.к. x = y и y>= 0.
Получим x = ([$8730$]21 + 1)/2.
Для второго случая x2 + x - 4 = 0.
Из двух корней -([$8730$]17+1)/2 и ([$8730$]17 -1)/2 этого уравнения условию y = -1 - x >= 0
удовлетворяет только отрицательный корень.
Ответ:
x1 = ([$8730$]21 +1)/2, x2 = -([$8730$]17 + 1)/2.
Обозначим [$8730$](x + 5) = y. Эта переменная удовлетворяет уравнению y2 - 5 = x и должна быть неотрицательной.
Система уравнений
y = x2 - 5, x = y2 - 5
эквивалентна исходному уравнению при условии y >= 0.
Вычитая из первого уравнения второе, получим
y - x = (x-y)(x+y), т.е,, должно быть либо y = x, либо y = -x - 1.
В первом случае имеем квадратное уравнение x2 - x - 5 = 0,
у которого отрицательный корень нужно отбросить, т.к. x = y и y>= 0.
Получим x = ([$8730$]21 + 1)/2.
Для второго случая x2 + x - 4 = 0.
Из двух корней -([$8730$]17+1)/2 и ([$8730$]17 -1)/2 этого уравнения условию y = -1 - x >= 0
удовлетворяет только отрицательный корень.
Ответ:
x1 = ([$8730$]21 +1)/2, x2 = -([$8730$]17 + 1)/2.
5
Форма ответа
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